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Uniqueness and stability for the recovery of a time-dependent source in elastodynamics

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  • This paper is concerned with inverse source problems for the time-dependent Lamé system in an unbounded domain corresponding to either the exterior of a bounded cavity or the full space $ {\mathbb{R}}^3 $. If the time and spatial variables of the source term can be separated with compact support, we prove that the vector valued spatial source term can be uniquely determined by boundary Dirichlet data in the exterior of a given cavity. Uniqueness and stability for recovering some class of time-dependent source terms are also obtained by using, respectively, partial and full boundary data.

    Mathematics Subject Classification: Primary: 65M32, 35R30; Secondary: 74B05.


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  • Figure 1.  Radiation of a source in an inhomogeneous isotropic elastic medium in the exterior of a cavity. Suppose that the cavity $ D $ is known. The inverse problem is to determine the source term from the data measured on $ \partial B_R = \{x\in {\mathbb{R}}^3: |x| = R\} $

    Figure 2.  Suppose that the data are collected on $ \omega $ and on $ \partial\Omega $. The inverse problem is to determine the value of $ g $ on $ \Omega $

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